Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Numerical Study of the Dynamic Response in Multi-Dofs Structures from the Seismic Excitation
Submission Author:
Patricia Grezelle , PR
Co-Authors:
Patricia Grezelle, Francisco Augusto Aparecido Gomes, PAOLA REGINA DALCANAL, Paulo Rogério Novak
Presenter: Patricia Grezelle
doi://10.26678/ABCM.COBEM2021.COB2021-1357
Abstract
Some engineering problems can be modeled mathematically using ordinary differential equations (ODEs), which allows evaluating the behavior of the physical phenomena of the problem. In this sense, the present study aims to compare the results from two solution methods, 4th-order Runge-Kutta Method and State-Space Method. The studied cases are structures with 1 and 2 degrees of freedom and a case with 3 degrees of freedom (DOFs) in a structure that receives excitation by the base through an already known seism. The Runge-Kutta Method consists of an explicit four-step method for the numerical solution of the set of ordinary differential equations, while the State-Space Method for a time-invariant linear system makes it possible to solve problems with multiple inputs and outputs in matrix form. In this way, the models will be discretized in a mass-spring-dampener system and then solved for both methods. With the responses of the two solutions, the Fast Fourier Transform (FFT) is applied to obtain the behavior of the structure in the frequency domain in order to verify the maximum amplitude of vibration. The calculations will be implemented in the Matlab software. The results of the numerical simulations are compared in terms of displacement and speed in the time and frequency domain.
Keywords
4th-order Runge-Kutta Method, State-Space Method, fast Fourier transform, dynamic analysis, Seismic Excitation
